SOLUTION: calculus-rate of change
A pulley system on a pier is used to pull boats towards the pier for docking. Suppose that a boat is being docked and has a rope attaching the boat's bow
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A pulley system on a pier is used to pull boats towards the pier for docking. Suppose that a boat is being docked and has a rope attaching the boat's bow
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Question 914105: calculus-rate of change
A pulley system on a pier is used to pull boats towards the pier for docking. Suppose that a boat is being docked and has a rope attaching the boat's bow on one end and feeding through the pier's pulley system on the other end. The pulley system is 1 meter higher than the height of the boat's bow. The rope is being pulled in at a rate of 1 m/s. When the boat is 6 meters from the pier, how fast is the boat approaching the pier? (Give your answer correct to five decimal places.)
You can put this solution on YOUR website! A pulley system on a pier is used to pull boats towards the pier for docking. Suppose that a boat is being docked and has a rope attaching the boat's bow on one end and feeding through the pier's pulley system on the other end. The pulley system is 1 meter higher than the height of the boat's bow. The rope is being pulled in at a rate of 1 m/s. When the boat is 6 meters from the pier, how fast is the boat approaching the pier? (Give your answer correct to five decimal places.)
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x = boat's distance
r = rope length
Get the distance as a function of the rope length.
Differentiate wrt time.
dx/dt = (1/2)*2r*(r^2 + 1)^(-1/2)*(dr/dt)
@ r = sqrt(37):
dx/dt = sqrt(37)/sqrt(38)
=~ 0.98675 m/sec
